A proof of the Krzyz conjecture

Abstract

A proof of the Krzyz conjecture is presented, based on the application of the variational method, as well as on the use of two classical results and some of their consequences. The mentioned results are the Caratheodory-Toeplitz criterion of continuing a polynomial to a Caratheodory class function, and the Riesz-Fejer theorem about trigonometric polynomials. This is an English translation of a preprint originally published in Russian: https://preprints.ru/article/1799

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